Solve 7⁴ × 8³ × (1/7)⁴: Power and Reciprocal Multiplication

Question

7483(17)4=? 7^4\cdot8^3\cdot(\frac{1}{7})^4=\text{?}

Video Solution

Solution Steps

00:00 Simply
00:06 When there's a fraction with an exponent, both numerator and denominator are raised to that power
00:15 We'll use this formula in our exercise
00:21 Let's reduce what we can
00:29 1 raised to any power is always equal to 1
00:35 And this is the solution to the question

Step-by-Step Solution

We use the formula:

(ab)n=anbn (\frac{a}{b})^n=\frac{a^n}{b^n}

We decompose the fraction inside of the parentheses:

(17)4=1474 (\frac{1}{7})^4=\frac{1^4}{7^4}

We obtain:

74×83×1474 7^4\times8^3\times\frac{1^4}{7^4}

We simplify the powers: 74 7^4

We obtain:

83×14 8^3\times1^4

Remember that the number 1 in any power is equal to 1, thus we obtain:

83×1=83 8^3\times1=8^3

Answer

83 8^3